Texture distorted on UV unwrapped face
The diagonal line is caused by unproperly scaled UV coordinates for the face. Original face resembles trapeze where the bottom parallel line is longer and the top one - shorter. In order to avoid any distortions of the texture the UV map for that rectangle should also have those forms - one side shorter than the parallel one. 

If scaling unchanged UV map you'll notice how it distorts:



The easiest solution would be to unwrap again in order to restore original proportions. However you can scale those edges on the map to roughly respect original ratio as well.